Stampacchia引理、推广及应用

doi:10.3969/j.issn.1000-1565.2021.05.004

河北大学学报(自然科学版) ›› 2021, Vol. 41 ›› Issue (5): 481-487.DOI: 10.3969/j.issn.1000-1565.2021.05.004

Stampacchia引理、推广及应用

高红亚¹, 高斯宇²

收稿日期:2021-02-07 出版日期:2021-09-25 发布日期:2021-09-28
通讯作者: 高斯宇(1997—)
作者简介:高红亚(1969—),男,河北顺平人,河北大学教授,主要从事偏微分方程研究.E-mail: ghy@hbu.cn
基金资助:
国家自然科学基金资助项目(12071021);河北省自然科学基金资助项目(A2019201120)

Stampacchia lemma, generalizations and application

GAO Hongya¹, GAO Siyu²

1. Hebei Key Laboratory of Machine Learning and Computational Intelligence, College of Mathematics and Information Science, Hebei University, Baoding 071002, China; 2. Department of Mathematics, University of North Texas, Denton 76203, USA

Received:2021-02-07 Online:2021-09-25 Published:2021-09-28

摘要/Abstract

摘要： 经典的 Stmapacchia 引理在椭圆型偏微分方程的正则性理论和变分问题中有广泛应用.本文总结 Stampacchia 引理和此引理的若干推广,并给出这些推广在某退缩椭圆型偏微分方程正则性理论中的应用.

关键词: Stampacchia引理, 推广, 椭圆型偏微分方程, 变分问题, 正则性

Abstract: The classical Stampacchia lemma has been widely used in the regularity theory of elliptic partial differential equations and systems as well as variational problems. This paper summarizes the Stampacchia lemma and their generalizations, and give an application to the regularity theory of degenerate elliptic partial differential equations.

Key words: Stampacchia lemma, generalization, elliptic partial differential equation, variational problems, regularity

中图分类号:

O175.23

高红亚, 高斯宇. Stampacchia引理、推广及应用[J]. 河北大学学报(自然科学版), 2021, 41(5): 481-487.

GAO Hongya, GAO Siyu. Stampacchia lemma, generalizations and application[J]. Journal of Hebei University(Natural Science Edition), 2021, 41(5): 481-487.

参考文献

[1] STAMPACCHIA G. Regularisation des solutions de problemes aux limites elliptiques a données discontinues [J].Proceedings of the International Symposium on Linear Spaces, 1961, 2(1): 339-408.
[2] STAMPACCHIA G. Équations elliptiques du second ordreà coficients discontinus [J]. Séminaire Jean Leray, 1963, 3(1): 1-77.
[3] BOCCARDO L. The summability of solutions to variational problems since Guido Stampacchia [J].Rev R Acad Cien Serie A Mat, 2003, 97(1): 413-421.
[4] ALVINO A, BOCCARDO L, FERONE V, et al. Existence results for nonlinear elliptic equations with degenerate coercivity[J]. Ann Di Matematica Pura Ed Appl, 2003, 182(1): 53-79. DOI:10.1007/s10231-002-0056-y.
[5] BOCCARDO L, CROCE G. Elliptic partial differential equations [M]. Berlin: De Gruyter, 2014.
[6] BOCCARDO L, GIACHETTI D. Existence results via regularity for some nonlinear elliptic problems[J]. Commun Partial Differ Equ, 1989, 14(5): 663-680. DOI:10.1080/03605308908820624.
[7] BOCCARDO L, GALLOUET T, MARCELLINI P. Anisotropic equations in [J]. Differential Integral Equations, 1996, 9(1): 209-212.
[8] CIRMI G R, LEONARDI S. Regularity results for the gradient of solutions linear elliptic equations with L ^1, λ data[J]. Ann Di Matematica Pura Ed Appl, 2006, 185(4): 537-553. DOI:10.1007/s10231-005-0167-3.
[9] GAO H Y, DI Q H, MA D N. Integrability for solutions to some anisotropic obstacle problems[J]. Manuscripta Math, 2015, 146(3): 433-444. DOI:10.1007/s00229-014-0705-7.
[10] GAO H Y, LIU C, TIAN H.Remarks on a paper by Leonetti and Siepe [J]. J Math Anal Appl, 2013, 401(2): 881-887.
[11] GAO H Y, LEONETTI F, WAGN L H. Remarks on Stampacchia Lemma [J]. J Math Anal Appl, 2018, 458(1):112-122. DOI: 10.1016/j.jmaa.2017.08.056.
[12] INNAMORATI A, LEONETTI F. Global integrability for weak solutoins to some anisotropic elliptic equations [J]. Nonlinear Anal, 2015, 113(1): 430-434. DOI: 10.1016/j.na.2014.09.027.
[13] KOVALEVSKY A A. Integrability and boundedness of solutions to some anisotropic problems [J]. J Math Anal Appl,2015, 432(2):820-843. DOI: 10.1016/j.jmaa.2015.07.013.
[14] KOVALEVSKII A A, VOITOVICH M V. On the improvement of summability of generalized solutions of the Dirichlet problem for nonlinear equations of the fourth order with strengthened ellipticity[J]. Ukrainian Math J, 2006, 58(11): 1717-1733. DOI:10.1007/s11253-006-0164-8.
[15] LEONETTI F, SIEPE F. Global integrability for minimizers of anisotropic functionals[J]. Manuscripta Math, 2014, 144(1/2): 91-98. DOI:10.1007/s00229-013-0641-y.
[16] LEONETTI F, SIEPE F. Integrability for solutions to some anisotropic elliptic equations [J].Nonlinear Analysis, 2012, 75(5): 2867-2873. DOI: 10.1016/j.na.2011.11.028.
[17] GAO HY, HUANG M M, REN W. Regularity for entropy solutions to degenerate elliptic equations [J].J Math Anal Appl, 2020, 491(1): 124251. DOI: 10.1016/j.jmaa.2020.124251.
[18] GAO H Y, DENG H, HUANG M M, et al. Generalizations of Stampacchia lemma and applications to quasilinear elliptic systems [J].Nonlinear Analysis, 2021, 208(1):112297. DOI: 10.1016/j.na.2021.112297.
[19] BOCCARDO L, DALLAGLIO A, ORSINA L. Existence and regularity results for some elliptic equations with degenerate coercivity [J]. Atti Sem Mat Fis Univ Modena, 1998, 46(1): 51-81. (

Stampacchia引理、推广及应用

Stampacchia lemma, generalizations and application

PDF (PC)

可视化

摘要/Abstract

引用本文

使用本文

参考文献

相关文章 7

编辑推荐

Metrics

本文评价

[1]	黄苗苗,赵雪漪,冯贺平. 一类非线性椭圆问题解的正则性[J]. 河北大学学报(自然科学版), 2023, 43(3): 225-229.
[2]	黄苗苗,王凤莉,高红亚. Holder不等式的推广及应用[J]. 河北大学学报(自然科学版), 2019, 39(6): 568-572.
[3]	张琪,王莲虹,高红亚. 熵解的一个正则性结果[J]. 河北大学学报(自然科学版), 2019, 39(2): 113-117.
[4]	高红亚,乔金静. 微分形式障碍问题解的正则性[J]. 河北大学学报(自然科学版), 2011, 31(5): 453-455.
[5]	张艳慧,叶国妍. 半平面中推广的Poisson积分的渐进性质[J]. 河北大学学报(自然科学版), 2009, 29(1): 19-21,44.
[6]	安敏,高红亚,刘红. 非齐次A-调和方程障碍问题解的局部正则性[J]. 河北大学学报(自然科学版), 2005, 25(2): 140-143.
[7]	高红亚,高春霞. 空间拟正则映射理论与相关问题[J]. 河北大学学报(自然科学版), 2003, 23(4): 440-444.